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Generalized Poisson integer-valued autoregressive processes with structural changes.

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Summary
This summary is machine-generated.

This study presents a new generalized Poisson autoregressive process for modeling integer time series with piecewise structures and overdispersion. The model offers a robust framework for analyzing complex count data patterns.

Keywords:
Structural changes INAR modelsbinomial thinninggeneralized poisson distributionmoments targeting estimationnon-stationary process

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Count Data Modeling

Background:

  • Integer-valued time series often exhibit complex structures like piecewise behavior and overdispersion.
  • Existing models may not adequately capture these combined characteristics.
  • Accurate modeling is crucial for understanding and predicting phenomena involving counts.

Purpose of the Study:

  • Introduce a novel first-order generalized Poisson integer-valued autoregressive process.
  • Provide a flexible model for integer time series with piecewise structures and overdispersion.
  • Develop and analyze statistical estimation methods for the proposed model.

Main Methods:

  • Derivation of basic probabilistic and statistical properties of the new process.
  • Development of conditional least squares and conditional maximum likelihood estimators.
  • Establishment of asymptotic properties for the derived estimators.

Main Results:

  • The proposed generalized Poisson integer-valued autoregressive process effectively models piecewise structures and overdispersion.
  • Theoretical properties of the estimators are rigorously established.
  • Numerical simulations and a real data example demonstrate the model's practical applicability.

Conclusions:

  • The new model provides a valuable tool for analyzing overdispersed integer-valued time series with piecewise dynamics.
  • The derived estimation methods are statistically sound and practically implementable.
  • This work contributes to the advancement of statistical modeling for discrete time series data.